Although I'm sure with christmas they have had their fill of cookies, you can always whip up a batch of sugar cookies and have them decorate them. You probably have sprinkles and chocolate chips lying around the house they can use so you don't have to get out. You don't even have to roll and cut them just make them into balls and flatten them out before you bake.
"Horns" with TP or paper towel tubes is good. Just have them color on them or use stickers and they can make their own noise through them!
My kids love to make placemats. That would be fun to do for the new year. Just use a sheet of construction paper (maybe tape 2 together if necessary) and have the kids decorate with crayons, markers, stickers, etc. You can cut out shapes from other pieces of paper that they can glue on too.
Or if you have any diaper boxes or cereal boxes lying around cut them into rectangles, squares or circles, cut a hole in the center and have them decorate a picture frame. They could even put a picture from tonight or tomorrow to commemorate the new year. Dried pasta and buttons would be fun to use for decoration.